Two-dimensional Phononic Crystals Research Articles

Mechanical metastructure with embedded phononic crystal for flexural wave attenuation

Destructive interference-based metamaterials have shown excellent characteristics in elastic wave manipulation and vibration attenuation. Nevertheless, challenges persist in the application due to limited space and lightweight design, as current metastructures require additional beam structure. To simplify the design of metamaterials for flexural wave manipulation, this paper presents a new class of embedded phononic crystal for manipulating flexural wave propagation in both one and two-dimensional space by taking advantage of destructive interference, which can effectively suppress the mechanical vibration of a beam structure with a broad band gap. The flexural wave dispersion characteristic in a non-uniform beam structure is derived based on the Euler–Bernoulli beam theory, and an embedded phononic structure with the mechanism of destructive interference is presented to demonstrate its effectiveness in mitigating mechanical vibration. Subsequently, four typical units of embedded phononic structures are designed for attenuating flexural wave propagation in a beam structure. Finally, both numerical simulations, including one and two-dimensional phononic crystals, and physical experiments are implemented to evaluate the performance of the presented metastructure for flexural wave manipulation, which indicates that the proposed embedded phononic structures can effectively mitigate structural vibration in the low-frequency domain. To the best of our knowledge, it is the first attempt to design the metabeam with embedded phononic structures by taking advantage of destructive interference.

Effects of void geometry on two-dimensional monolithic porous phononic crystals

Phononic crystals are renowned for their distinctive wave propagation characteristics, notably bandgaps that offer precise control over vibration phenomena, positioning them as a critical material in advanced vibro-elastic engineering and design. We investigate how pore shapes influence the bandgap in continuum two-dimensional phononic crystals made from a single material. Using the square lattice and unit cells with fourfold symmetry, our numerical analyses reveal that the normalized gap size is highly dependent on the minimum ligament width in the structure. Additionally, we find that fine geometric features represented by higher-order Fourier coefficients decrease the gap size. This study offers insight into the design of phononic crystals and vibro-elastic metamaterials for precise wave control through void patterning.

Topology optimization of two-dimensional magnetorheological elastomer phononic crystal plate with tunable bandgap considering a specified target frequency

Topology optimization of two-dimensional magnetorheological elastomer phononic crystal plate with tunable bandgap considering a specified target frequency

Type-II Dirac phonons in a two-dimensional phononic crystal

We explore the distinctive properties associated with a type-II Dirac point in a simply structured phononic crystal with a lattice deformation. This type-II Dirac point emerges at the Brillouin zone boundary, resulting from the lifting of two degenerate bands and featuring a conical-like Fermi surface in the equi-frequency curve. A practical implementation of such a phononic crystal is achieved with LEGO bricks. Upon introducing a periodic parity-time (PT) symmetric non-Hermitian perturbation, the phononic crystal undergoes a transition from PT-symmetric phase to PT-broken phase, causing the deformation of type-II Dirac point into an oval of exceptional points in the band structure. Based on the eigenmodes of the type-II Dirac point, a k⃗⋅p⃗ perturbation theory can be used to characterize these systems before and after the phase transition. Using a scattering matrix, we analyze the symmetric and broken phases and demonstrate that broadband unidirectional transparency and a coherent perfect absorber and laser can be realized with such a phononic crystal slab.

Dual-Channel Underwater Acoustic Topological Rainbow Trapping Based on Synthetic Dimension

The concept of “rainbow trapping” has generated considerable interest in wave propagation and energy harvesting, offering new possibilities for diverse and efficient acoustic wave operations. In this work, we investigate a dual-channel topological rainbow trapping device implemented within an underwater two-dimensional phononic crystal based on synthetic dimension. The topological edge states with different frequencies are separated and trapped at different spatial locations. Acoustic waves propagate simultaneously along two boundaries due to the degeneracy of the edge states. In particular, the propagation of a dual-channel topological rainbow is also realized by using a bend design. This work contributes to the advancement of multi-channel devices in synthetic space and provides a reference for the design of highly efficient underwater acoustic devices.

Collective radial breathing modes in homogeneous nanotube bundles

We present a Raman study of the collective vibrations arising from the homogeneous bundling of single-walled carbon nanotubes and analyze the dependence of their vibrational coupling on the tube diameter using two systems, single-walled carbon nanotube coils and a monochiral carbon nanotube film. We report on two breathing-like modes for quasi-infinite bundles, compared to the single radial breathing mode characteristic for isolated tubes. The exciton-phonon coupling in these modes is probed with resonant Raman spectroscopy, revealing the same resonance energy for both breathing-like peaks. Our experimental findings align well with previously reported theoretical studies, demonstrating a 1/d scaling for all modes, as well as confirming the relative shift of the modes dependent on intertube interaction. These vibrations provide insight into the role of intertube lattice dynamics in two-dimensional THz-range phononic crystals.

Band structure calculations of three-dimensional solid-fluid coupling phononic crystals using dual reciprocity boundary element method and wavelet compression method

The algorithm for calculating the band structures of two-dimensional phononic crystals (PCs) using the boundary element method (BEM) has been proposed for many years. However, it has not yet been extended to three-dimensional (3D) PCs because the fundamental solutions of 3D dynamics are complex and are related to angular frequency. In this study, the BEM is applied to calculate the band structures of 3D solid-fluid coupling PCs by combining the dual reciprocity method. The use of the dual reciprocity method can help avoid nonlinear eigenvalue problems. To address the limitation of fully populated matrices in BEM, the wavelet compression method based on B-spline wavelet on the interval is adopted. Some small matrix entries, which are generated by the vanishing moment and local support characteristics, are set to zero using the provided truncation technique. This process results in the production of sparse matrices. The constructed generalized linear eigenvalue equations are modified to tackle the ill-conditioned matrix issues arising from the distinct fundamental solutions of solids and fluids. The results show that this method is superior to the finite element method in terms of calculation efficiency. Compared to conventional BEM, the current wavelet BEM can not only generate sparse matrices but also reduce the integration calculation time when handling large-scale problems.

Experimental demonstration of rainbow trapping of elastic waves in two-dimensional axisymmetric phononic crystal platesa).

Structures with specific graded geometries or properties can cause spatial separation and local field enhancement of wave energy. This phenomenon is called rainbow trapping, which manifests itself as stopping the propagation of waves at different locations according to their frequencies. In acoustics, most research on rainbow trapping has focused on wave propagation in one dimension. This research examined the elastic wave trapping performance of a two-dimensional (2D) axisymmetric grooved phononic crystal plate structure. The performance of the proposed structure is validated using numerical simulations based on finite element analysis and experimental measurements using a laser Doppler vibrometer. It is found that rainbow trapping within the frequency range of 165-205 kHz is achieved, where elastic waves are trapped at different radial distances in the plate. The results demonstrate that the proposed design is capable of effectively capturing elastic waves across a broad frequency range of interest. This concept could be useful in applications such as filtering and energy harvesting by concentrating wave energy at different locations in the structure.

Topological rainbow trapping of elastic waves in two-dimensional valley phononic crystal plates

Rainbow trapping is a significant strategy for capturing waves of different frequencies at different spatial positions. It offers significant potential for multi-frequency on-chip nanophotonic devices in the era of big data and has attracted much interest recently, and topological rainbow trapping that is immune to disorder has been observed in optics and acoustics. Reported here is the topological rainbow trapping of elastic waves using gradient valley phononic crystal plates (PCPs) with a hexagonal lattice, based on valley edge states that are localized at the boundary between two PCPs with opposite valley topological phases. The gradient valley PCPs are achieved by gradually adjusting the height of the scatterers or the thickness of the PCPs. The topological rainbow trapping of elastic waves is shown by applying vertical vibration to the studied gradient PCPs, which are simple in structure and easily fabricated, providing a good solution for manipulating and trapping elastic waves.

Graphene-based phononic crystal lenses: Machine learning-assisted analysis and design

The advance of artificial intelligence and graphene-based composites brings new vitality into the conventional design of acoustic lenses which suffers from high computation cost and difficulties in achieving precise desired refractive indices. This paper presents an efficient and accurate design methodology for graphene-based gradient-index phononic crystal (GGPC) lenses by combing theoretical formulations and machine learning methods. The GGPC lenses consist of two-dimensional phononic crystals possessing square unit cells with graphene-based composite inclusions. The plane wave expansion method is exploited to obtain the dispersion relations of elastic waves in the structures and then establish the data sets of the effective refractive indices in structures with different volume fractions of graphene fillers in composite materials and filling fractions of inclusions. Based on the database established by the theoretical formulation, genetic programming, a superior machine learning algorithm, is introduced to generate explicit mathematical expressions to predict the effective refractive indices under different structural information. The design of GGPC lenses is conducted with the assistance of the machine learning prediction model, and it will be illustrated by several typical design examples. The proposed design method offers high efficiency, accuracy as well as the ability to achieve inverse design of GGPC lenses, thus significantly facilitating the development of novel phononic crystal lenses and acoustic energy focusing.

Stable Acoustic Pulling in Two-Dimensional Phononic Crystal Waveguides Based on Mode Manipulation

Acoustic manipulation is a set of versatile platforms with excellent manipulation capabilities. In recent years, researchers have increasingly achieved specific manipulations beyond the translation and capture of particles. Here, we focus on the acoustic field momentum mechanism that generates an acoustic radiation force (ARF). A phononic crystal (PC) waveguide is established to amplify the forward momentum of the acoustic beam through the mode conversion of the acoustic field. Based on the conservation of momentum, the object gains reverse momentum. Thus, acoustic pulling can be achieved through the mode conversion of the acoustic field. Furthermore, we analyze the ARFs of two identical objects. It turns out that they can be manipulated separately by opposing forces. Our study provides a new way to achieve stable long-range acoustic pulling, and will explore, beneficially, the interaction between acoustic waves and matter.

Acoustic 4 × 2 encoder based on linear waveguides in two-dimensional solid-solid phononic crystals

The paper proposes a design for an acoustic 4 × 2 encoder that incorporates acoustic waveguides within a two-dimensional square lattice phononic crystal structure. The encoder's structure comprises of a nylon matrix embedded with a 33 × 30 molybdenum rod array, featuring four input ports and two output ports. The simulation results demonstrate that the proposed structure can effectively achieve the acoustic 4 × 2 encoder functionality. To evaluate the performance of the acoustic 4 × 2 encoder, we analyzed the transmission spectrum using the finite element method (FEM).

Effect of surface/interface stress on nanoscale phononic crystals using complete Gurtin-Murdoch model

The gradual miniaturization of acoustic devices requires us to study phononic crystals (PCs) at nanoscale, which should consider the effect of surface/interface stress. The first key point in this study is the complete use of the Gurtin-Murdoch model, and thereby the treatment of the surface displacement gradient term, which was avoided by all previous work on the nanoscale PCs. The second key point is that the dual reciprocity boundary element method is first applied to analyze the band structures of two-dimensional nanoscale PCs. The effect of surface/interface stress on band structures is discussed by investigating four typical nanoscale systems: nanoholes in a soft matrix, nanoholes in a stiff matrix, soft nanoscatterers in a stiff matrix and stiff nanoscatterers in a soft matrix. The numerical results demonstrate that the band structures obtained applying complete Gurtin-Murdoch model ascend comparing with those using simplified model, which enhances theoretical basis for designing nanoscale PCs. Furthermore, the effect of surface displacement gradient term is not obvious for the last three systems, and the displacement gradient term and surface tension should be ignored simultaneously when simplifying calculations. This study can provide good support for the control of hypersound at nanoscale.

Pushing the limits of complete omnidirectional bandgaps in 2D nonsymmorphic single-phase phononic crystals

We expand the limits of complete omnidirectional bandgaps (neither P- nor S-waves can propagate) for high symmetry two-dimensional phononic crystal (PnC) designs. We reveal an extremely large 124% complete omnidirectional bandgap and demonstrate the possibility of creating custom, mechanically robust PnCs with improved characteristics via simple geometric changes to known PnC designs. The findings are experimentally validated, proving that it is feasible to achieve extreme ultrasonic attenuation using the nonsymmorphic p4gm symmetry group design, for both P- and S-waves, which significantly outperforms symmorphic p4mm-group PnC designs. We shed light on the high attenuation properties of the p4gm PnC for S-waves (which is rarely explored experimentally), revealing differences between the mode types. Practical insight into the design of PnCs with improved acoustic properties for potential applications in the field of vibration isolation, most notably when S-wave elimination is vital, is discussed.

Active control of localized mode and transmission in topological phononic waveguides by non-Hermitian modulation

We demonstrate the switching behavioral differences between lossy and nearly lossless edge-mode propagation by non-Hermitian modulation based on the phononic band design of a C 3v symmetric, two-dimensional phononic crystal with a unit cell composed of three air-filled circular holes in polydimethylsiloxane. We numerically show that strong loss effects lead to the extinction of the localized modes. This mechanism is analogous to the bound-to-unbound transition in non-Hermitian quantum systems. This result suggests that large variations in non-Hermitian modulation can be used for the active control of edge-mode propagation along topological interfaces.

Predicting Band Structures of Two-Dimensional Phononic Crystal Slab for Sensor Predesigning Based on Artificial Neural Network

Predicting Band Structures of Two-Dimensional Phononic Crystal Slab for Sensor Predesigning Based on Artificial Neural Network

Multi-objective optimized design of two-dimensional multi-phase phononic crystals with materials self-selection

In this paper, the multi-objective optimization problem (MOOP) of selecting suitable materials from four materials for phononic crystals layouts is investigated based on an optimization method combined nondominated sorting-based genetic algorithm II (NSGA-II) and finite element method (FEM). Driven by different optimization objectives, the changes in the optimized structure compared to the seed structure are the change of the bandgap mechanism from a local resonance mechanism to a Bragg scattering mechanism, the change of the included materials from four to three, and the significant change in the location and extent of the pores and other materials, respectively. The obtained nondominated Pareto solution of MOOP can balance the bandgap and the structural mass, which provides the decision-maker trade-off to select the appropriate optimized solution. Compared with the single-objective optimization problem (SOOP), the MOOP not only obtains a nondominated solution close to the result of SOOP, but also obtains other nondominated solutions of MOOP, which proves the effectiveness of the optimization algorithm in this paper. The design method in this paper can be easily extended to select suitable materials from a wider variety of materials for bandgap optimization design of PnCs, which has very promising applications.

Topological Design of Two-Dimensional Phononic Crystals Based on Genetic Algorithm.

Phononic crystals are a kind of artificial acoustic metamaterial whose mass density and elastic modulus are periodically arranged. The precise and efficient design of phononic crystals with specific bandgap characteristics has attracted increasing attention in past decades. In this paper, an improved adaptive genetic algorithm is proposed for the reverse customization of two-dimensional phononic crystals designed to maximize the relative bandwidth at low frequencies. The energy band dispersion relation and transmission loss of the optimal structure are calculated by the finite-element method, and the effective wave-attenuation effect in the bandgap range is verified. This provides a solution for the custom-made design of acoustic metamaterials with excellent low-frequency bandgap sound insulation or other engineering applications.

Edge and corner states in two-dimensional finite phononic crystals: Simulation and experimental study

We investigate the mechanical vibration transmission in two-dimensional infinite and finite phononic crystals (PCs). The infinite PC consists of a periodic structure formed by square plates connected to the center of each of their nearest neighbors through a tiny beam. Numerical simulations using finite elements show a wide full bandgap for frequencies between 27 kHz and 32 kHz, approximately. Acoustic resonant spectroscopy was used to measure the PC frequency spectra for the different vibrations, using a finite PC consisting of 8 by 8 cells, which was designed with the same configuration as the infinite one. Experimental results corroborate the existence of a full complete bandgap predicted by the numerical method. However, the width was significantly reduced due to the appearance of edge and corner states. The border states were obtained numerically using a supercell. The measured wave amplitudes and the simulated ones present a great similarity. Some states appear located at the corners of the finite PC demonstrating that zero-dimensional states can also appear in two-dimensional phononic crystals.

Research on Bulk Acoustic Wave Resonator Based on Phononic Crystal

Abstract With the continuous advancement of information technology and the rapid development of mobile communication technology, from smart home to automatic driving of cars, and then to the application and development of virtual reality, communication technology has evolved from the earliest communication between people to communication between things. The frequency band supported by smart phones and various small mobile terminals is increasing, and their communication frequency is also gradually increasing, which brings some challenges to the traditional RF front-end devices. The traditional RF filter can not meet the current market demand because of its own performance and size constraints. As the best option to integrate with RF circuit or microwave circuit, bulk acoustic wave filter has great development and application prospects in modern RF communication system. This paper will focus on the solid-state assembled resonators based on one-dimensional and two-dimensional phononic crystals, analyze the influence and change law of the performance of bulk acoustic wave devices based on two-dimensional phononic crystals, then explore the main loss mechanism existing in solid-state assembled devices, and propose improvement schemes, which lays a foundation for the application of solid-state assembled resonators in today’s RF front-end.